The 18-year-old dispatched 2011 French Open champion Na 6-4, 6-7 (5-7) 6-2, two days after her shock second-round win against Kim Clijsters sent the three-time Flushing Meadows champion into retirement.

Robson, the world No.89, set the tone with an early break and although beaten on a second set tie-break, the Olympic mixed doubles silver medallist outplayed Chinese world No.8 Na to take the deciding set.

She becomes the first British woman to make the fourth round at a grand slam since Sam Smith at Wimbledon in 1998 and the first in New York since Jo Durie 21 years ago.

Robson, who now faces defending champion Sam Stosur, said: ‘I knew if I kept sticking with her and playing my shots it might pay off, and it did.

‘I had a few break points early on and I gave them up with some average returning, so when I got a chance I knew I had to go for it.’

Against Clijsters, Robson took time to settle, but she found an early rhythm, breaking Na with a crunching return to take a 2-0 lead in the first set.

Na served twice to stay in the match before the second set went to a tie-break, which she won at the first opportunity with a superb backhand.

Prodigious ball-striking saw Robson force two successive breaks in the final set, and a big serve on match point sealed another notable scalp.